I hear you. I haven't met a ton of people out in the profession who are UK grads but Edward Blum does really good work so that's a testament to the program.
If you're interested in the Civil War era, you may want to consider Northwestern, NYU, and UC Davis. Princeton could also be interesting. Matt Karp is doing really good work and is likely to get tenure. Also, there's probably not a better person on 19th century black life than Tera Hunter right now. 10 years ago I would have told you to seriously consider Maryland but all their folks who work on emancipation and the Civil War are on the verge of retirement.
Another program with a southern history focus that is on the rise is Rice. Their program has an explicit southern history focus, good funding, and connections to the Journal of Southern History.